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A photon has energy of 1 × 10^{18} eV - AQA - A-Level Physics - Question 8 - 2020 - Paper 1

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A photon has energy of 1 × 10^{18} eV. An object of mass 0.03 kg has kinetic energy equal to the energy of the photon. What is the speed of the object?

Worked Solution & Example Answer:A photon has energy of 1 × 10^{18} eV - AQA - A-Level Physics - Question 8 - 2020 - Paper 1

Step 1

Calculate the energy of the photon

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Answer

The energy of the photon is given as ( E = 1 \times 10^{18} ) eV. To convert this to joules, use the conversion factor ( 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} ):

E=1×1018 eV×1.6×10−19 J/eV=1.6×10−1 J=0.16 JE = 1 \times 10^{18} \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = 1.6 \times 10^{-1} \text{ J} = 0.16 \text{ J}

Step 2

Use the kinetic energy formula

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Answer

The kinetic energy (KE) of an object is calculated using the formula:

KE=12mv2KE = \frac{1}{2} mv^2

Where:

  • ( KE ) is the kinetic energy,
  • ( m ) is the mass of the object,
  • ( v ) is the speed of the object.

In this case, we set ( KE = 0.16 \text{ J} ) and ( m = 0.03 \text{ kg} ).

Step 3

Solve for the speed of the object

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Answer

Rearranging the formula gives:

v=2×KEm  ⟹  v=2×0.160.03v = \sqrt{\frac{2 \times KE}{m}} \implies v = \sqrt{\frac{2 \times 0.16}{0.03}}

Calculating the value:

v=0.320.03≈10.67≈3.26 m/sv = \sqrt{\frac{0.32}{0.03}} \approx \sqrt{10.67} \approx 3.26 \text{ m/s}

Thus, the speed of the object is approximately ( 3 \text{ m/s} ), which corresponds to option B in the choices provided.

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